Differential Calculus
Paper Code:
MAT102
Credits:
3
Contact Hours:
45.00
Max. Marks:
100.00
Objective:
o To introduce basics in mathematics.
o To improve analytical skill.
Unit I:
I
12.00
Mean Value theorems (Lagrange’s, Cauchy, Taylor’s and Maclaurins with different remainders). Expansion of sin x, cos x, e^x, log(1+x), (1+x)m.
Unit II:
II
12.00
Derivative of an arc, Intrinsic equation of the curve, Pedal equation (Cartesian & Polar Curves) Curvature
Unit III:
III
12.00
Partial differentiation, Total derivative , Euler’s theorem for homogeneous functions, Maxima and Minima of functions of two independent variables – necessary and sufficient conditions (without proof), Lagrange’s undetermined multipliers (without proof) and simple problems.
Unit IV:
IV
12.00
Envelopes, Asymptotes. (Cartesian and Polar curves).
Unit V:
V
12.00
Multiple points, Classification of double points –Node, cusp, points of inflexion.
Tracing of curves: Cartesian and Polar form.
Essential Readings:
- Shanti Narayan, Differential Calculus, S.Chand and Co., New Delhi.
- M. Ray & G.C. Sharma, Differential Calculus, Shivlal agarwal & Co. Agra.
- Gorakh Prasad, Text Book on Diff.Calculus, Pothishala Pvt.Ltd, Allahabad.
- Chaurasia, Goyal, Agarwal , Jain ; Diff. Calculus, RBD, Jaipur.
References:
- Theory and problems of Advanced Calculus, Schaum’s outline series New York.
- H.S. Dhami, Differential Calculus,New Age Int. Ltd., New Delhi.
- Akhtar & Ahsan, A text Book of Differential Calculus, PHI Ltd., New Delhi.
- G.N.Berman, A Problem book in Mathematical Analysis, Mir Publishers, Moscow.
Academic Year:
